27,531 views
32 votes
32 votes
A RAM chip has a capacity of 1024 words of 8 bits each (1K × 8). The number of 2 × 4 decoders with enable line needed to construct a 16K × 16 RAM from 1K × 8 RAM is

(A) 4      (B) 5      (C) 6      (D) 7

4 Answers

Best answer
51 votes
51 votes
Actually we need decoders for selection of a row from address lines not data lines.

So you have to concentrate upon the first term of each of RAM size and chip size which are 16 K and 1 K respectively.

So no of address lines  =  16K / 1K

                                  =   16

Hence we can use 4 : 16 decoder for this .But we have to realise this using 2 : 4 decoder.

So this question now becomes actually of realisation of 4 : 16 decoder using 2 : 4 decoders.

So 4 decoders are required in inner level as from 1 2:4 decoder we have only 4 output lines whereas we need 16 output lines.

Now to point to these 4 decoders , another 2 : 4 decoder is required in the outer level .

Hence no of 2 : 4 decoders to realise the above implementation of RAM  = 1 + 4  

                                                                                                          =  5

Hence B) is the correct answer.
selected by
43 votes
43 votes

No. of 1K x 8 chips required = $\frac{16K * 16}{1K * 8}$

                                         = 16 * 2 chips ( Each row has two 1K*8 chips and a total of 16 rows)

Now, in order to access this bigger memory we need to choose one of the 16 rows.

Let us see how many address lines are required :

Total memory = 16K * 16

                    = 16K words ($\because$ 1 word = 16 bits here)

                    = $2^{14}$

Hence 14 address lines are needed to access the memory. Let the address be represented by A13A12...A1A0

We can observe that we need 10 address bits to access each of the 1K * 8 Chip 

Remaining Address bits = 14 - 10

                                   = 4 Address bits

Let us suppose we use the least 10 bits to address 1K*8 chip (Since it has 1024 words, we need 10 bits).

We can implement the decoders using the Higher 4 bits as shown in the picture (Picture is self Explanatory)

34 votes
34 votes
Number of chips required =(16K*16)/(1K*8)=16*2 (i.e 16 chips vertically with each having 2 chips horizontally. So to select one chip out of 16 vertical chips, we need 4 x 16 decoder. Available decoder is – 2 x 4 decoder, to be constructed is 4 x 16 decoder
So 16/4=4, 4/4=1 Hence 4+1=5 decoders.
16 votes
16 votes

Hence, a total of 5 Decoders are required.

answer = option B

Answer:

Related questions

28 votes
28 votes
3 answers
2
Arjun asked Sep 23, 2014
8,191 views
In the following truth table, $V = 1$ if and only if the input is valid.$$\begin{array}{cc}\textbf{Inputs}&\textbf{Outputs}\\ \begin{array}{|c|c|c|c|} \hline{D_0}&D_1&D_2...
31 votes
31 votes
7 answers
3
Arjun asked Sep 24, 2014
9,394 views
Which one of the following expressions does NOT represent exclusive NOR of $x$ and $y$?$xy + x′ y′$$x\oplus y′$$x′\oplus y$$x′\oplus y′$
21 votes
21 votes
2 answers
4
Arjun asked Sep 23, 2014
7,231 views
The smallest integer that can be represented by an $8\text{-bit}$ number in $2's$ complement form is$-256$$-128$ $-127$$0$